X-ray diffraction method

ABSTRACT

An X-ray diffraction method for the analysis of polycrystalline materials, the method comprising: (a) providing a polycrystalline material for analysis; (b) providing a polychromatic X-ray source, wherein the source produces X-rays by accelerating charged particles to energies of no more than 1 MeV; (c) collimating X-rays from the polychromatic X-ray source into a beam having a divergence in the range of from 10 −4  to 10 −2  radians; (d) exposing at least a portion of the polycrystalline material to the collimated X-ray beam, whereby the beam is diffracted; (e) collecting at least some of the diffracted X-rays in an energy dispersive X-ray detector or array; and (f) analysing the collected, diffracted X-rays.

The present invention relates to the field of X-ray diffraction ofcrystalline materials and, in particular, to an X-ray diffraction methodfor the determination of structural and/or chemical characteristics ofpolycrystalline engineering materials and components formed therefrom.

X-rays are electromagnetic radiation having a wave length of from 10⁻¹¹to 10⁻⁹ m and produced by bombardment of atoms by high-quantum-energyparticles. In practice, X-rays may be produced by bombarding a metaltarget, for example copper or tungsten, with fast electrons in a vacuumtube.

The principle of X-ray generation in a vacuum tube is schematicallyillustrated in FIG. 1. Electrons are emitted by the heated cathode (Ca)and accelerated by the applied voltage towards the anode (oranti-cathode, Ac) target. There they undergo rapid deceleration andabsorption processes, which result in the emission of X-rays.

The radiation emitted as a result of the collision between electrons andthe metal target can be separated into two components: (i) a continuousspectrum, which is spread over a wide range of wavelengths (also knownas Bremsstrahlung); and (ii) a superimposed line spectrum, which isdetermined by the materials of the target (also known as thecharacteristic radiation).

The use of X-ray diffraction is of great importance in the analysis ofcrystals. For example, in the fields of metallurgy and materialsscience, X-ray diffraction techniques may be used to identify thelattice parameter and the structure of metal crystals. Additionally, thetechniques may be used to identify the arrangement of different kinds ofatoms in crystals, the presence of imperfections, the orientation ofgrains, the size of grains, the size and density of precipitates and thestate of lattice distortion.

Known X-ray diffraction techniques include the Laue method, the rotatingcrystal method and the powder method (also known as the Debye/Scherrermethod).

In the Laue method a stationary single crystal is bathed in a beam ofpolychromatic radiation. This method is used for determining theorientation of single crystals and the study of crystal imperfections.

In the rotating crystal method a single crystal is rotated in a beam ofmonochromatic X-rays. This method is also used for the determination ofcrystal structures.

In the powder method a powdered polycrystalline sample is bathed in abeam of monochromatic radiation. This method is used for thedetermination of lattice parameters, grain sizes and the preferredorientation of grains.

The powder method is also used to study bulk polycrystalline samples,such as engineering components and structures. For example, it can beused to determine the lattice parameter variation in orientation andposition, and to deduce sample strain and stress.

Conventional laboratory diffraction measurements rely on interrogatingonly a thin (≈<50 μm) surface layer of the sample. Accordingly, suchtechniques do not provide information regarding stresses and strains insub-surface regions or in the bulk of a sample.

Another widespread application of X-rays in industry and medicine isradiography, i.e. for transmission photography to obtain absorptioncontrast-images. The only property of the X-ray radiation that isutilised in such applications is the penetrating ability.

In standard radiographic set-up, industrial tungsten target X-ray tubesare used to produce polychromatic radiation within a widely divergent(˜40°) cone.

In defectoscopic configuration, the object of study, for example analuminium casting, is bathed in an incident X-ray beam, and aphotographic plate or CCD camera is used to record the image whichregisters the attenuation of the beam along the path between the sourceand any given pixel. This set-up is only capable of providinginformation on relatively large defects (typically about a millimetre insize), such as casting voids.

For the purpose of quantitative diffraction analysis, the radiationproduced by an industrial X-ray tube is not well suited in that it has adefinition that is too poor both in terms of wave length (energy) andwave vector (direction).

The present invention aims to address at least some of the problemsassociated with the prior art.

In a first aspect the present invention provides an X-ray diffractionmethod for the analysis of polycrystalline materials, the methodcomprising:

-   (a) providing a polycrystalline material for analysis;-   (b) providing a polychromatic X-ray source, wherein the source    produces X-rays by accelerating charged particles to energies of no    more than 1 MeV;-   (c) collimating X-rays from the polychromatic X-ray source into a    beam having a divergence in the range of from 10⁻⁴ to 10⁻² radians;-   (d) exposing at least a portion of the polycrystalline material to    the collimated X-ray beam, whereby the beam is diffracted;-   (e) collecting at least some of the diffracted X-rays; and-   (f) analysing the collected, diffracted X-rays.

The following discussion applies to all aspects of the present inventionunless otherwise stated.

The source preferably produces X-rays by accelerating charged particlesto energies of no more than 500 keV, more preferably to no more than 400keV, still more preferably to no more than 300 keV. The source willtypically comprise means to accelerate electrons in a vacuum tube toimpact a metal target.

The X-ray beam typically has a brilliance ≦10¹² photons/s/mm²/mrad²/0.1%BW.

The diffracted X-rays may suitably be collected by an energy dispersiveX-ray detector or array. For example, a Li-drifted Si or Ge solid statedetector may be used. The energy dispersive X-ray detector typically hasa relative energy resolution of 0.5×10⁻² to 4×10⁻², more typically1×10⁻² to 3×10⁻². An example of a suitable detector is the Canberra BEGeliquid nitrogen cooled, solid state energy dispersive germanium crystalX-ray and gamma-ray detector, in combination with multi-channelanalyser, computer acquisition software and hardware.

The energy of the collimated X-ray beam is preferably ≧60 keV, morepreferably in the range of from 100 to 300 keV. This enables thecollimated X-ray beam to penetrate the polycrystalline material to adepth of typically ≧1 mm, preferably ≧5 mm, more preferably, ≧10 mm,still more preferably ≧15 mm. Indeed, the attenuation depth can be up to50 mm or more depending on the polycrystalline material. Thus,sub-surface X-ray analysis may be achieved. The attenuation depth is thethickness of material such that the transmitted beam intensity is equalto 37% of the incident beam intensity.

As mentioned above, the X-ray source will typically comprise means toaccelerate electrons in a vacuum tube to impact a metal target. In thismanner, a metal target is bombarded with fast electrons. The X-raysource is preferably an industrial X-ray-source (for example a tungstentarget X-ray tube) such as may be used in standard radiographicapplications. A suitable example is a 160 kV, 1.6 kW industrial X-raysource (W tube) by Philips, supplied by AT Roffey Ltd (circa 1980).

The beam may be collimated using known techniques. For example, a pairof adjustable copper-tungsten X-ray slits may be used.

The method may further comprise moving the collimated X-ray beamrelative to the polycrystalline material. In a preferred embodiment, thecollimated X-ray beam is scanned across at least a portion of thepolycrystalline material, while keeping the polycrystalline materialstationary. This is advantageous in circumstances where thepolycrystalline material forms part of a relatively large engineeringcomponent. In such cases, movement of the component would be difficult.

The collected, diffracted X-rays may be analysed in order to determine astructural and/or chemical characteristic of the polycrystallinematerial, for example lattice parameter determination. In turn, latticeparameter determination may be used to provide information on stressesand/or strains in the polycrystalline material and, preferably, to mapstresses and/or strains. Stresses and/or strains in the bulk of thepolycrystalline material may be mapped at a depth of typically ≧1 mm,preferably ≧5 mm, more preferably ≧10 mm, still more preferably ≧15 mm.Indeed, stresses and/or strains in the bulk of the polycrystallinematerial may be mapped at a depth of up to 50 mm or more depending onthe polycrystalline material. This is in contrast to the conventionallaboratory techniques where only a thin surface layer is analysed.

The polycrystalline material may be a natural object or an engineeringarticle or component part thereof. The polycrystalline material willtypically comprise a metal or alloy, a ceramic or a crystalline polymeror a composite crystalline material, such as, for example, a ceramicreinforced metal matrix composite material. An example is SiC reinforcedAl.

The polycrystalline material will typically have a thickness of ≧0.1 mm,more typically ≧1 mm, still more typically ≧5 mm, still more typically≧10 mm, still more typically ≧15 mm. Indeed, the polycrystallinematerial may have-a thickness of up to 50 mm or more depending on theabsorption.

In contrast to the conventional powder diffraction techniques, thepolycrystalline material need not be in the form of a fine grainedpowder, nor is material removal, cutting or drilling of any kindrequired within the region of interest. The method according to thepresent invention therefore allows engineering components to be analysedin their intended structural form. This is important for the measurementof sub-surface engineering stresses and strains.

In a second aspect, the present invention provides an apparatus forX-ray diffraction analysis of polycrystalline materials, the apparatuscomprising:

-   (i) a polychromatic X-ray source, wherein the source produces X-rays    by accelerating charged particles to energies of no more than 1 MeV;-   (ii) means for collimating X-rays from the polychromatic X-ray    source into a beam having a divergence in the range of from 10⁻⁴ to    10⁻² radians;-   (iii) an energy dispersive X-ray detector or array for collecting at    least some of the diffracted X-rays resulting, in use, from exposing    at least a portion of a polycrystalline material to the collimated    X-ray beam; and-   (iv) means for analysing the collected, diffracted X-rays.

The polychromatic source may be moveable with respect to apolycrystalline material to be analysed. Advantageously, the collimatedX-ray beam is adapted, in use, to scan, across the sample of thepolycrystalline material, while the polycrystalline material ismaintained stationary.

In the method and apparatus according to the present invention thepolycrystalline material (for example a component or sample) ispreferably maintained stationary, while an X-ray probe is moved aroundit. The probe may comprise the X-ray source and the detector, which maybe fixed relative to each other on a rigid arm.

In a third aspect, the present invention provides a method ofquantitatively mapping the sub-surface distribution of the crystallattice parameter in a polycrystalline material, the method comprising:

-   (a) providing a sample for analysis, wherein the sample comprises a    polycrystalline material;-   (b) providing a polychromatic X-ray source, wherein the source    produces X-rays by accelerating charged particles to energies of no    more than 1 MeV;-   (c) collimating X-rays from the polychromatic X-ray source into a    beam having a divergence in the range of from 10⁻⁴ to 10⁻² radians    and an attenuation length typically ≧1 mm;-   (d) scanning the collimated X-ray beam across the sample, whereby    the beam is diffracted;-   (e) collecting at-least some of the diffracted X-rays in an energy    dispersive X-ray detector or array; and-   (f) analysing the collected, diffracted X-rays to map the lattice    parameter in the polycrystalline material.

The polycrystalline material may be a natural material or,alternatively, an engineering material, including a component formedtherefrom.

This method may preferably be used to determine the stresses and/orstrains in polycrystalline natural or engineering materials andcomponents formed therefrom. Accordingly, a preferred further step (f)involves transforming the map of the lattice parameter into a map ofsub-surface engineering stresses and/or strains.

The technique of composite strain mapping is described in ScriptaMaterialia, Vol. 39, No. 12, pp. 1075-1712, 1988.

Typically, the present invention achieves a strain measurement accuracyof 50×10⁻⁶ to 200×10⁻⁶, more typically 100×10⁻⁶ to 150×10⁻⁶. The spatialresolution is typically, from 0.25 mm to 1 mm.

Whole pattern fitting may be applied to extract extremely accuratevalues of the lattice parameter (better than 5×10⁻⁵) and hence residuallattice strain.

The present invention will now be described further with reference tothe following drawings, in which:

FIG. 1 is a schematic illustration of the process of X-ray generation ina vacuum tube;

FIG. 2 shows a diffraction configuration used in the Example (from rightto left: incident beam—slits—sample—slits—detector);

FIG. 3 shows the X-ray source spectrum (energy) used in the Example;

FIG. 4 shows the ‘no sample’ source pattern (lattice spacing) used inthe Example;

FIG. 5 shows a scattering pattern of a polycrystalline Al alloy sampleused in the Example (log scale, counts);

FIG. 6 shows a scattering pattern of a polycrystalline Al alloy sampleused in the Example (linear scale, counts);

FIG. 7 shows a Gaussian fit to the Al diffraction peak 1 (the box on theright gives the values and errors of the parameters);

FIG. 8 shows a Gaussian fit to the Al diffraction peak 2 (the box on theright gives the values and errors of the parameters); and

FIG. 9 shows an example of a multiple peak pattern that can be obtainedfrom an aluminium alloy sample.

EXAMPLE

Transmission polychromatic X-ray diffraction experiments were carriedout on 1.5 mm thick samples of rolled Al sheet. The strain accuracyachieved (prior to optimization) was approximately 150×10⁻⁶. Thiscorresponds to a stress accuracy of ≈10 MPa in aluminium, ≈14 MPa incopper, and ≈28 MPa in steel.

The experimental set-up comprised:

-   a) A 160 kV, 1.6 kW industrial X-ray source (W tube) by Philips,    supplied by AT Roffey Ltd (circa 1980), placed in a lead-lined room    and position-controlled remotely using a traverse motor assembly;-   b) A Canberra BEGe liquid nitrogen cooled, solid state energy    dispersive germanium crystal X-ray and gamma-ray detector, in    combination with multi-channel analyser, computer acquisition    software and hardware; and-   c) A pair of adjustable (0.5 to 5 mm) composite (copper tungsten)    X-ray slits.

For the purpose of spatial definition the beam was collimated using twolarge blocks of lead, about 50 mm thick, which only allowed radiationthrough a long slit, 0.5 mm wide. This set-up was used in thediffraction experiment. However, a secondary slit was needed to furtherdefine the beam direction, and also as an anti-scatter device. The twoslits were aligned using a laser pointer. Similarly, a pair of slits wasused on the detector side to provide directional definition. In bothcases the slits were mounted at two ends of a copper tube. Copper, agood photon absorber, was used to reduce secondary scatter.

While the incident beam was close to horizontal, the diffracted beam wasdefined to be inclined at an angle of about 6.2°.

A schematic illustration of the set-up is shown in FIG. 2.

The lead block surfaces were irradiated by the intense incident X-raybeam and thus fluoresced (i.e. absorbed and re-emitted X-rays) at thecharacteristic wavelengths (energies) of Pb. This is evidenced by theenergy spectrum shown in FIG. 3. The characteristic energies present dueto the ‘source’ * properties do not change with the scattering angleprescribed by the set-up. However, the peaks of energy corresponding todiffraction from the crystal lattice of the sample depend on thescattering angle through Bragg's equation: 2 dsin θ=nλ=hc/f. Thisallowed the scattering angle to be adjusted so as to avoid, as far aspossible, overlap with the ‘signature’ peaks of lead. Given a certainscattering angle θ, the energy pattern is converted to the latticeparameter pattern using Bragg's equation. For the configuration used,θ=3.1°, and the ‘no sample’ pattern is shown in FIG. 4.

The sample was then placed at the intersection of the incident andscattered beams. The sample contributed to the flux into the detector,through diffraction on many individual grains. New peaks appear in thepattern. This is illustrated in FIG. 5, where a logarithmic scale isused for the vertical axis to make the peak at approximately 2.3 Å moreprominent. FIG. 6 shows the same profile using a linear vertical scalefor the counts.

Although the aluminium diffraction peak at approximately 2.3 Å in FIG. 6appeared broad and small, fitting it with a simple Gaussian functiondemonstrated that it provided acceptable accuracy. The Gaussian peakshape used for this peak (dubbed ‘Peak 1’) was described by thefunction:m2*exp(−(m0−m1)ˆ2/2/m3ˆ2)+m4

Here m0 is the argument (lattice spacing) and m1 to m4 are the functionparameters that are sought. The values of the parameters given aboverepresent the initial guesses. The result of fitting is shown in FIG. 7:Gaussian fit to the Al diffraction peak 1. The box on the right givesthe values and errors of the parameters.

The fitting result corresponds to a strain accuracy ofΔd/d=0.00033441/2.3304=145×10⁻⁶. This corresponds to a stress accuracyof about 10 MPa in aluminium, 14.5 MPa in copper, and 29 MPa in steel.

The lattice spacing of 2.330 Å is close to the value of 4.05/√3=2.338 Åfor the (111) reflection in Al. The next reflection, (200), is expectedat a lattice spacing of 4.05/2=2.025 Å. Close inspection of FIG. 6 doesindeed show that a peak exists at approximately 2 Å in that pattern, butis overlapped by a characteristic twin of lead. However, provided thistwin is ignored in the analysis, this peak can be fitted as well, asshown in FIG. 8: Gaussian fit to the Al diffraction peak 2. The box onthe right gives the values and errors of the parameters.

The fitting result for peak 2 corresponds to a strain accuracy ofΔd/d=0.0013964/2.0105=700×10⁻⁶. This corresponds to a stress accuracy ofabout 50 MPa in aluminium, 70 MPa in copper, and 140 MPa in steel. Theaccuracy is affected by the overlap with the characteristic twin of Pb.Information from multiple peaks may be combined to improve the overallaccuracy.

The lattice spacing of 2.01 Å is close to the value of 2.025 Å for the(200) reflection in Al. The ratio of the spacing for the two peaks is1.15, which is very close to the theoretically expected value of 1.156for the face centred cubic (fcc) lattice.

This Example demonstrates that the accuracy of, lattice parameterdetermination is adequate for engineering stress measurementapplications. The rate of data collection was approximately 15 minutesper pattern.

The method allows very efficient treatment of multiple peak diffractionpatterns. An example of a multiple peak pattern that can be obtainedfrom an aluminium alloy sample is shown in FIG. 9. Whole pattern fittingcan be applied to extract extremely accurate values of the latticeparameter (better than 5×10⁻⁵) and hence residual lattice strain.

In the present invention, polychromatic beam/energy dispersive detectorX-ray transmission experiments are used to analyse polycrystallineengineering materials and components.

The present invention provides a method of accurately determining thelattice parameter and thus stress measurements within the bulk ofpolycrystalline engineering materials and components. The presentinvention enables quantitative measurements of stresses (and preferredorientation) in components. This may be achieved by accuratedetermination of centre positions and intensities of multiplediffraction peaks, not just their identification. The entire (orsubstantially the entire) diffraction pattern that has been collectedmay be analysed.

High energy X-rays are used to penetrate a component or sample at verylow angles (transmission). Accurate beam collimation helps achieve theresolution required for three-dimensional mapping of stresses. Duringthis procedure, the component or sample may be maintained stationary,while an X-ray probe is moved around it. The probe comprises the X-raysource and detector fixed on a rigid arm thereby maintaining theirrelative positions fixed.

1. An X-ray diffraction method for the analysis of polycrystallinematerials, the method comprising: (a) providing a polycrystallinematerial for analysis; (b) providing a polychromatic X-ray source,wherein the source produces X-rays by accelerating charged particles toenergies of no more than 1 MeV; (c) collimating X-rays from thepolychromatic X-ray source into a beam having a divergence in the rangeof from 10⁻⁴ to 10⁻² radians; (d) exposing at least a portion of thepolycrystalline material to the collimated X-ray beam, whereby the beamis diffracted; (e) collecting at least some of the diffracted X-rays inan energy dispersive X-ray detector or array; and (f) analysing thecollected, diffracted X-rays.
 2. A method as claimed in claim 1, whereinthe source produces X-rays by accelerating charged particles to energiesof no more than 500 keV.
 3. A method as claimed in claim 1, wherein theenergy dispersive X-ray detector has a relative energy resolution offrom 0.5×10⁻² to 5×10⁻².
 4. A method as claimed in claim 1, wherein theenergy of the collimated X-ray beam is ≧60 keV, preferably in the rangeof from 100 to 300 keV.
 5. A method as claimed in claim 1, wherein thecollimated X-ray beam penetrates the polycrystalline material to anattenuation depth of ≧1 mm.
 6. A method as claimed in claim 1, furthercomprising moving the collimated X-ray beam relative to thepolycrystalline material.
 7. A method as claimed in claim 6, comprisingscanning the collimated X-ray beam across at least a portion of thepolycrystalline material, while keeping the polycrystalline materialstationary.
 8. A method as claimed in claim 1, wherein the collected,diffracted X-rays are analysed in order to determine a structural and/orchemical characteristic of the polycrystalline material.
 9. A method asclaimed in claim 8, wherein the structural characteristic is the latticeparameter.
 10. A method as claimed in claim 9, wherein lattice parameterdetermination is used to provide information on phase distributions,stresses and/or strains in the polycrystalline material.
 11. A method asclaimed in claim 10, wherein lattice parameter determination is used tomap phase distributions, stresses and/or strains in the polycrystallinematerial.
 12. A method as claimed in claim 11, wherein lattice parameterdetermination is used to map phase distributions, stresses and/orstrains in the polycrystalline material at a depth of ≧1 mm.
 13. Amethod as claimed in claim 1, wherein the polycrystalline material is anengineering article or component part thereof.
 14. A method as claimedin claim 1, wherein the polycrystalline material comprises a metal oralloy, ceramic or crystalline polymer, including combinations of two ormore thereof.
 15. A method as claimed in claim 1, wherein thepolycrystalline material is a composite material comprising acrystalline phase.
 16. A method as claimed in claim 15, wherein themetal matrix composite material is a glass and/or ceramic reinforcedmetal matrix composite material.
 17. A method as claimed in claim 1,wherein said portion of the polycrystalline material has a thickness of≧1 mm.
 18. An apparatus for X-ray diffraction analysis ofpolycrystalline materials, the apparatus comprising: (i) a polychromaticX-ray source, wherein the source produces X-rays by accelerating chargedparticles to energies of no more than 1 MeV; (ii) means for collimatingX-rays from the polychromatic X-ray source into a beam having adivergence in the range of from 10⁻⁴ to 10⁻² radians; (iii) an energydispersive X-ray detector or array for collecting at least some of thediffracted X-rays resulting, in use, from exposing at least a portion ofa polycrystalline material to the collimated X-ray beam; and (iv) meansfor analysing the collected, diffracted X-rays.
 19. An apparatus asclaimed in claim 18, wherein the polychromatic source is moveable withrespect to a polycrystalline material to be analysed.
 20. An apparatusas claimed in claim 18, wherein the collimated X-ray beam is adapted, inuse, to scan, across the polycrystalline material, while thepolycrystalline material is maintained stationary.
 21. A method ofquantitatively mapping the sub-surface distribution of the crystallattice parameter in a polycrystalline material, the method comprising:(a) providing a sample for analysis, wherein the sample comprises apolycrystalline material; (b) providing a polychromatic X-ray source,wherein the source produces X-rays by accelerating charged particles toenergies of no more than 1 MeV; (c) collimating X-rays from thepolychromatic X-ray source into a beam having a divergence in the rangeof from 10⁻⁴ to 10⁻² radians, and a penetration depth of ≧1 mm; (d)scanning the collimated X-ray beam across the sample, whereby the beamis diffracted; (e) collecting at least some of the diffracted X-rays inan energy dispersive X-ray detector or array; and (f) analysing thecollected, diffracted X-rays to map the lattice parameter in thepolycrystalline material.
 22. A method as claimed in claim 21, whereinthe polycrystalline material is a natural material or an engineeringmaterial, including a component formed therefrom.
 23. A method asclaimed in claim 21, further including: (f) transforming the map of thelattice parameter into a map of sub-surface engineering stresses and/orstrains.